{"id":"https://openalex.org/W2045622842","doi":"https://doi.org/10.1109/isccsp.2012.6217860","title":"Lack of spectral gap and hyperbolicity in asymptotic Erdo&amp;#x00A8;s-Renyi sparse random graphs","display_name":"Lack of spectral gap and hyperbolicity in asymptotic Erdo&amp;#x00A8;s-Renyi sparse random graphs","publication_year":2012,"publication_date":"2012-05-01","ids":{"openalex":"https://openalex.org/W2045622842","doi":"https://doi.org/10.1109/isccsp.2012.6217860","mag":"2045622842"},"language":"en","primary_location":{"id":"doi:10.1109/isccsp.2012.6217860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isccsp.2012.6217860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 5th International Symposium on Communications, Control and Signal Processing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083129277","display_name":"Onuttom Narayan","orcid":"https://orcid.org/0000-0001-8433-5569"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Onuttom Narayan","raw_affiliation_strings":["Department of Physics, University of California, Santa Cruz, USA","Department of Physics, University of California Santa Cruz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of California, Santa Cruz, USA","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"Department of Physics, University of California Santa Cruz","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084787837","display_name":"Iraj Saniee","orcid":"https://orcid.org/0000-0001-9162-9194"},"institutions":[{"id":"https://openalex.org/I72090969","display_name":"Nokia (United States)","ror":"https://ror.org/038km2573","country_code":"US","type":"company","lineage":["https://openalex.org/I2738502077","https://openalex.org/I72090969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Iraj Saniee","raw_affiliation_strings":["Bell Laboratories, Murray Hill, USA","Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Murray Hill, USA","institution_ids":[]},{"raw_affiliation_string":"Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill","institution_ids":["https://openalex.org/I72090969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083981154","display_name":"Gabriel H. Tucci","orcid":null},"institutions":[{"id":"https://openalex.org/I72090969","display_name":"Nokia (United States)","ror":"https://ror.org/038km2573","country_code":"US","type":"company","lineage":["https://openalex.org/I2738502077","https://openalex.org/I72090969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gabriel H. Tucci","raw_affiliation_strings":["Bell Laboratories, Murray Hill, USA","Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Murray Hill, USA","institution_ids":[]},{"raw_affiliation_string":"Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill","institution_ids":["https://openalex.org/I72090969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.0472,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.97905759,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6283198595046997},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5993385910987854},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.5256344676017761},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44493287801742554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42784371972084045},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.41245806217193604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4122960567474365},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1063501238822937}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6283198595046997},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5993385910987854},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.5256344676017761},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44493287801742554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42784371972084045},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.41245806217193604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4122960567474365},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1063501238822937},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isccsp.2012.6217860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isccsp.2012.6217860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 5th International Symposium on Communications, Control and Signal Processing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1552870256","https://openalex.org/W1565832774","https://openalex.org/W1578099820","https://openalex.org/W1973836644","https://openalex.org/W2018440517","https://openalex.org/W2031246048","https://openalex.org/W2032983973","https://openalex.org/W2044936155","https://openalex.org/W2088164510","https://openalex.org/W2098449770","https://openalex.org/W2134086356","https://openalex.org/W2138482845","https://openalex.org/W2151417892","https://openalex.org/W2566505556","https://openalex.org/W2905110430","https://openalex.org/W2963852017","https://openalex.org/W4235484205","https://openalex.org/W4252973173","https://openalex.org/W6675048992"],"related_works":["https://openalex.org/W3103885756","https://openalex.org/W2022507394","https://openalex.org/W3101494832","https://openalex.org/W3013650182","https://openalex.org/W4249605382","https://openalex.org/W2560376394","https://openalex.org/W822020258","https://openalex.org/W4299378864","https://openalex.org/W2953336627","https://openalex.org/W2963287622"],"abstract_inverted_index":{"We":[0,56],"show":[1],"that":[2,59,88],"the":[3,7,11,18,47,61,70],"normalized":[4],"Laplacian":[5],"of":[6,10,49,78],"giant":[8],"component":[9],"Erd\u00f6s-Renyi":[12,71],"random":[13,72],"graph":[14,73],"G(n,":[15],"pn)":[16],"in":[17,41,60],"regime":[19,62],"pn=":[20,63],"d/n":[21],"for":[22,65],"d":[23],"a":[24,50,75],"constant":[25],"greater":[26],"than":[27],"1":[28],"(sparse":[29],"regime)":[30],"has":[31,74],"zero":[32],"spectral":[33,51],"gap":[34,52],"as":[35,82],"n":[36,83],"\u2192":[37,84],"\u221e.":[38],"This":[39],"is":[40],"contrast":[42],"to":[43],"earlier":[44],"results":[45],"showing":[46,87],"existence":[48],"when":[53],"npn=":[54],"O(log2(n)).":[55],"also":[57],"prove":[58],"d/n,":[64],"any":[66],"\u03b4":[67],">;":[68],"0":[69],"positive":[76],"probability":[77],"containing":[79],"\u03b4-fat":[80],"triangles":[81],"\u221e,":[85],"thus":[86],"these":[89],"graphs":[90],"are":[91],"asymptotically":[92],"non-hyperbolic.":[93]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
